Problem: Simplify the following expression: $a = \dfrac{k^2 - 3k + 2}{k - 1} $
Explanation: First factor the polynomial in the numerator. $ k^2 - 3k + 2 = (k - 1)(k - 2) $ So we can rewrite the expression as: $a = \dfrac{(k - 1)(k - 2)}{k - 1} $ We can divide the numerator and denominator by $(k - 1)$ on condition that $k \neq 1$ Therefore $a = k - 2; k \neq 1$